Control method for processes of synthesis of chemical products

ABSTRACT

A control method for a process of synthesis of at least one chemical product in an equipment comprising at least one reactor (R) which is assimilated to a mixed reactor, in which manipulated variables (GC) allow to act on the course of the process in order to make one or more variables related to the properties of the product and/or to the running of the process, which are called controlled variables (GR).

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a control method for processes ofsynthesis of chemical products. It also relates to a control device formaking use of this method and to a process of synthesis, in particularof polymer, controlled by this method.

2. Description of the Background

In a process of synthesis of chemical products which is conductedconventionally, controllers of PID (proportional-integral-differential)type are used for controlling individually a larger or smaller number ofvariables (temperatures, flow rates, pressures, etc.) which affect thecourse of the synthesis. In other words, for of each temperature, flowrate or pressure to be controlled, its actual value is measuredcontinuously (or intermittently), and a PID controller compares thisactual value with a set point and acts on the variable to be controlledso as to reduce, if appropriate, the difference between the set pointand the measured value.

In view of the complexity of most industrial processes of chemicalsynthesis, the set points of the various controllers must today still beadjusted empirically in order to obtain finally the desired propertiesfor the synthesized product. Recipes are used for this purpose, whichprovide combinations of parameters determined empirically to obtain, ina steady state, the desired properties for the synthesized product.

Empirical relationships between the controlled variables and theproperties of the synthesized product could be deduced from theserecipes with the help of more or less sophisticated statistical tools.It is obvious, however, that these empirical relationships can hardlytake into account the many interdependencies which exist between thevarious variables which are controlled separately, or the unknownperturbations such as the impurity contents of the raw materials.

It is also obvious that a traditional closed-loop control, employingmeasurements of essential properties for the synthesized product asfeedback corrections, is difficult to apply to most processes ofsynthesis. This is because the dead times involved either in the processor in the measurements or analyses used as feedback corrections are toolong and the independences between the various variables ruling theprocess are too complex.

International Application WO 93/24533 describes a control method for aprocess of gas phase polymerization of an alpha-olefin in a horizontalreactor, in which control parameters make it possible to act on thecourse of the process in order to make the melt index (MFR) of thepolymer equal to the corresponding set point, the method including thefollowing steps:

determining the relationships between the melt index of the polymerleaving the reactor and a first series of parameters,

controlling this first series of parameters,

calculating the MFR of the polymer,

adapting at least one of the parameters so as to adjust the calculatedMFR to a predetermined value.

It has been known for a long time that processes of synthesis,especially processes of continuous polymer synthesis (polymerizationprocesses), equipped with controllers with empirically adjusted setpoints have major disadvantages which can be summarized as follows:

start-ups of the synthesis process take much time and produce largequantities of off-specification product;

grade changes are slow, which also results in the production of largequantities of transitional off-specification products;

the production rate of the process, that is to say the mass ofproduct(s) synthesized per time unit is difficult to chance withoutimpairing the properties of this or these products;

the consistency of the essential properties of the synthesizedproduct(s) is often poor, even in a steady state.

In order to avoid empirical adjusting of the set points, it has beenproposed in the specialist literature to use control methods forprocesses of synthesis which make use of characteristic equationsmodelling the process of synthesis in order to relate some properties ofthe synthesized product(s) to the running conditions of the reactor(s)during the synthesis. However, in order to limit the complexity of thesecharacteristic equations, it was hitherto considered that in practice itwas necessary either to consider solely the static case (steady state),or to limit one-self to a highly simplified empirical modelling of theprocess dynamics. The use of a static model is limited to the control ofa fairly steady state production.

In the case of empirical modelling the characteristic equations arevalid only for a narrow range of validity (near the point where themodelling has been performed). In both cases the start-up phases and thetransition phases are poorly controlled. It is undoubtedly possible toenvisage "covering" a wider range of operating conditions by undertakingsuch local modelling at several different points in the region of theoperating parameters, but such an approach becomes prohibitive as soonas an attempt is made to control a number of variables by acting on manyparameters.

It would consequently be desirable to have available a control methodand a control device which are simple and better adapted to thespecificities of the dynamics of processes of synthesis of chemicalproducts.

SUMMARY OF THE INVENTION

To this end, the present invention relates to a control method for aprocess of synthesis of at least one chemical product in an equipmentcomprising at least one reactor (R) which can be assimilated to aperfectly mixed reactor, in which one or more manipulated variables (GC)make it possible to act on the course of the process in order to makeone or more variables related to the properties of the product and/or tothe course of the process, which are called controlled variables (GR),equal to the corresponding set points (C_(GR)) (or at least as close aspossible to the latter), the said method including the following steps:

(a) input of set points concerning the controlled variables (C_(GR));

(b) computation, by means of a prediction unit (OP), of predictions ofthe controlled variables (P_(GR)), based on measurements of the processmanipulated variables (M_(GC));

(c) use of a control unit (OC) to compute the set points of the processmanipulated variables (C_(GC)), based on the set points (C_(GR)) and thepredictions (P_(GR)) of the controlled variables;

(d) transmission of the set points of the process manipulated variables(C_(GC)) to actuators, or to control units controlling the actuators, inorder to act on the course of the process;

in which the prediction unit (OP) is based on a mathematical model ofthe process, called a direct model (M) and is designed in such a waythat the mass M_(XR) of at least one constituent (X) in the reactor (R)is predicted by the equation:

    M.sub.XR =LAG(F.sub.XRin ·τ.sub.X, τ.sub.X)

in which:

F_(XRin) is the mass flow rate of the constituent X entering the reactorR;

τ_(X) is the residence time of X in the reactor (time constant), whichis

    τ.sub.X =M.sub.XR /(ΣFxdis)

in which:

M_(XR) denotes the last calculated value of the mass of the constituentX present in the reactor R;

Σ Fxdis denotes the sum of all the mass flow rates Fxdis at which theconstituent X disappears from the reactor R, especially by reactionand/or by leaving the reactor;

the function y=LAG (u, τ) is the solution of the differential equation##EQU1## calculated with the instantaneous value of u and of τ, and withthe last calculated value of y.

DETAILED DESCRIPTION OF THE INVENTION

The advantage of this method is that the abovementioned differentialequation is solved by a simple algebraic calculation, for example usingthe following formula (T denoting the time interval, generally small inrelation to τ, separating the successive calculations) or using aformula equivalent to the latter: ##EQU2##

In the case where the masses of several constituents are evaluated asset out above, the method of the invention is particularly advantageousinsofar as these masses can be calculated sequentially by such simplealgebraic calculations, recalculated frequently (in general T<<τ). Onthe other hand, traditional methods require the simultaneous solving ofa system of differential equations, and this generally requires a highcalculating power and sophisticated algorithms of numerical calculation(integration); as a result, each iteration of calculation takes a longtime and consequently a control of this type reacts badly to rapidvariations.

The controlled process of synthesis can be used for the synthesis of amonomeric or polymeric compound; very good results have been obtained inthe case of the control of polymerization processes. The process alsoextends to the case where a number of useful products are synthesizedsimultaneously in the same process. The process may be continuous ornoncontinuous (batch); the control method of the invention givesexcellent results in the case of continuous processes. The controlledprocess of synthesis may optionally constitute only a part of a vasterprocess, the other parts of which are controlled differently or are notcontrolled. In order for the control method of the invention to beapplicable it is necessary that at least one reactor may be assimilatedto a perfectly mixed reactor, that is to say a reactor in which thevarious variables (temperature, concentrations of the constituentspresent, and the like) are virtually identical at each point. Otherpossible reactors may be of the piston (plug flow) type; they aremodelled mathematically using dead times. The method is also applicableto a process taking place in a number of reactors arranged in seriesand/or in parallel, capable of producing products with identical ordifferent properties.

"Constituents" is intended to denote all of the substances present inthe reactor and intended to take part in the synthesis or to permit it:not only the starting reactants as well as the synthesized product(s),but also any substance(s) not undergoing any conversion, such assolvents, catalysts, and the like.

In addition to one or more reactors, the plant in which the processtakes place may optionally include other conventional devices such aspressure-reducing valves, strippers, condensers, driers, distillationcolumns and the like. These auxiliary devices can furthermore generallyalso be considered to be reactors (perfectly mixed or of plug flowtype), even if no chemical reaction takes place therein.

In the case of a polymerization process the "variables related to theproperties of the product" may, for example, be chosen from themolecular mass, the melt index, the standard density, the comonomercontent when a comonomer is present, and the like.

Examples of "variables related to the process" are especially thetemperature and the pressure prevailing in the reactor, the productionrate of the process, the concentrations of the various reactants in thereactor, and the like. The production rate denotes the mass of productsynthesized per unit time, which is however not necessarily equal to theflow rate of synthesized product leaving the reactor: thus, by way ofexample, especially in the start-up phases, the mass flow rate ofsynthesized product leaving the reactor is generally very low, or evenzero, although the synthesis has begun, that is to say that this exitflow rate is then lower than the production rate. On the other hand, ina steady state the production rate can be assimilated to the mass ofproduct synthesized per unit time.

Examples of "manipulated variables" are flow rates of reactants enteringthe reactor, the power supplied to the heating devices, and the like.These are variables which make it possible to act on the course of theprocess as well as, generally, the properties of the synthesizedproduct.

The set point or points of the manipulated variable or variables aretransmitted directly or indirectly to conventional actuators such asespecially valves, heating units, and the like. "Indirectly" means thatthe manipulated variables can be transmitted through the intermediacy ofone or more control units (generally controlling a single variable, e.g.PID controllers), controlling the actuator or actuators ("local"control).

Insofar as hardware is concerned, the prediction unit and the controlunit are generally conventional computing devices enabling calculationsto be performed as a function of their cabling or their programming;they may in particular be computers or digital systems forcommand-control (SNCC). A single device may advantageously combine theprediction and control functions. The computing device or devices usedare preferably of the digital type and supply the results of theircalculations at regular intervals (intermittently). The time intervalsseparating the supply of these results may vary with time and may alsodiffer according to the result involved: it is clear that rapidlyvarying variables must be recalculated more frequently than slowlyvarying variables. Shift registers may be employed for materiallysimulating the dead times.

The prediction unit is based on a direct mathematical model of theprocess (M), in which the reactor (R) is assimilated to a perfectlymixed reactor; one or more pure delays (dead times) may optionally betaken into account to represent possible reactors of plug flow type,possible transport delays or delays in obtaining results ofmeasurements, etc.

The control unit is preferably based on the reverse of the direct modelemployed in the prediction unit (reverse model).

In general the sum Σ Fxdis of all the mass flow rates (Fxdis) at whichthe constituent X disappears from the reactor R includes two terms:

F_(RX), which denotes the mass flow rate at which X is consumed in oneor more possible chemical reactions;

F_(Xout), which denotes the possible mass flow rate of X leaving thereactor by drawing-off during the reaction, in the (usual) case where Xis not entirely consumed by reaction in this reactor; or else, forexample, by evaporation, in the case of an open reactor.

The advantage of the method is that the Fxdis terms are generallyproportional to M_(XR) ; for example, in general

    F.sub.Xout =M.sub.XR /τ.sub.R

(τ_(R) denoting the residence time of the reactor R)

and

    F.sub.RX =R.sub.X ·M.sub.XR

(R_(X) denoting the reactivity of X in the reactor R). In this case theexpression which gives τ_(X) is simplified and becomes:

    τ.sub.X =1/(R.sub.X +1/τ.sub.R)

This expression is independent of M_(XR), and this constitutes anextremely advantageous simplification.

Another advantage of the method lies in the periodic calculation of theresidence time τ_(X). Actually, τ_(X) represents well the dynamics ofthe constituent considered in the reactor. This makes it possibleespecially to follow the change in this parameter, which is importantfor understanding the dynamics of the process, and consequently for itscontrol. On the other hand, the empirical methods of "black box" type donot make it possible to gain access to this parameter.

The calculation of the predictions of the controlled variables (P_(GR))may advantageously additionally take into account one or moremeasurements of controlled variables (M_(GR)), of manipulated variables(M_(GC)) and/or of other variables related to the running of the process(M_(AP)).

Similarly, advantageously, the calculation of the set points of theprocess manipulated variables (C_(GC)) may additionally take intoaccount one or more measurements of controlled variables (M_(GR)), ofmanipulated variables (M_(GC)) and/or of other variables related to therunning of the process (M_(AP)) which are identical with or differentfrom those optionally taken into account for the calculation of thepredictions of the controlled variables (P_(GR)).

All the measurements which are discussed in the present description arenot necessarily direct measurements, in the sense that one or more ofthem may possibly be inferential measurements, that is to say valuesobtained by calculation from one or a number of other directmeasurements. Thus, for example, the production rate of some exothermicprocesses of synthesis cannot be measured directly, but an inferentialmeasurement thereof can be obtained by calculation, for example from(direct) measurements of the flow rate and of the entry and exittemperatures of the coolant fluid.

In the particular case of polymerization processes the property orproperties of the polymer involved in the control are preferably chosenfrom the specific density (SD) of the polymer, the rheologicalproperties of the polymer melt, and its comonomer content. Inparticular, the rheological property or properties involved in thecontrol method are advantageously the melt index of the polymer and/or aviscosity measurement.

One or more properties of the polymer are advantageously evaluated byemploying a technique chosen from near infrared spectroscopy (NIR),Fourier transform infrared spectroscopy (FTIR) and nuclear magneticresonance (NMR).

In particular, one or more properties of the polymer can beadvantageously evaluated by applying a preestablished correlationrelationship to the results of measurements carried out by near infraredspectroscopy (NIR) at a number of wavelengths predetermined as afunction of the nature of the polymer and chosen between 0.8 and 2.6 um.

Further details concerning the carrying out of such measurements in thecontext of the control of polymerization processes can be found inPatent Application EP 328826 (U.S. Pat. No. 5,155,184).

In order to take account of possible deviations between the measurementsand the predictions of the controlled variables it may be useful toresort to a correction.

A first type of correction consists in correcting the set point of atleast one controlled variable (C_(GR)) on the basis of the(advantageously filtered) deviation between the measurement (M_(GR)) andthe prediction (P_(GR)) of this controlled variable, so as to make thecontrol effective (M_(GR) =C_(GR)) even in the presence of an error inthe prediction of this controlled variable. This technique is commonlyreferred to by the expression "internal model control" (IMC).

A second type of correction consists in periodically adapting the model(M) of the process on the basis of the (advantageously filtered)deviation between the predictions (P_(GR)) and the measurements (M_(GR))of the controlled variables, such that, here as well, the model of theprocess should supply predictions of the controlled variables (P_(GR))which are as near as possible (ideally equal) to the measurements ofthese variables (M_(GR)), and this is essential for an efficaciouscontrol.

The adaptation consists in recalibrating the model, that is to say inrecalculating one or more of its parameters; normally the number ofrecalculated parameters does not exceed the number of controlledvariables for which both a prediction and a measurement are available. Aresynchronization (shift in time) of these measurements is oftendesirable, above all when they are measurements of properties of thesynthesized product which take a long time to obtain. This second typeof correction is more advantageous, insofar as it allows the model to bealso adapted in respect of its dynamics.

The adaptation relates not only to the direct model of the process(prediction unit), but also to the reverse model (control unit).

According to an advantageous alternative form the measurements (M_(GR))of the controlled variables are involved only in the optional adaptationof the model of the process and are not directly involved in thecalculation of the set points of the manipulated variables of theprocess (C_(GC)).

That is to say that the measurements of the controlled variables are notinvolved in the actual control: the advantage of this is that thequality of the control is thus not affected by the possible slowness ofthe evaluation of the product properties.

Another aspect of the invention relates to a control method as describedabove, applied to a polymerization process, including one or more of thefollowing additional steps:

calculation of a set point of temperature in the reactor as a functionof one or more set points of the product properties; and transmission oftemperature set point to one or more actuators making it possible tomodify the temperature in the reactor (possibly indirectly, that is tosay through the intermediacy of one or more control units, e.g. PIDcontrollers, controlling the actuator(s));

calculation of a heat balance for the reactor, based especially ontemperature measurements; use of this heat balance so as to determinethe quantity of polymer synthesized per time unit (production rate)and/or the catalyst efficiency and/or the concentration of at least onereactant in the reactor;

calculation of the quantity of heat produced by the polymerization, by acalculation of the quantity of the reactant or reactants whichpolymerize; determination by this means of the quantity of heat whichmust be added or removed to maintain the reactor temperature; use of theresult of the said calculation (for example by feed-forward) to improvethe temperature control, so as to conform as well as possible to the setpoint of temperature, especially in case of changes in the productionrate.

These alternative forms are based on the relation which exists betweenthe quantity of the reactant s) taking part in the reaction and thequantity of heat produced or absorbed by the reaction.

According to an advantageous alternative form the property Px_(R) of aconstituent "x" in the reactor R, which is assimilated to a perfectlymixed reactor, is calculated as follows:

    Px.sub.R =LAG(Px.sub.IN, Mx.sub.R /Fx.sub.IN)

where

"Px" is a property of a constituent "x", corresponding substantially tothe linear mixing law Px₁₊₂ =w₁ ·Px₁ +w₂ ·Px₂,

w₁ and w₂ being the mass fractions of two mixed fractions 1 and 2 ofproperty Px₁ and Px₂ (w₁ +w₂ =1);

Px₁₊₂ is the property of x as it leaves the reactor after mixing;

Px_(IN) is the property of the constituent "x" as it enters the reactorR;

Mx_(R) is the mass of the constituent x in the reactor R;

Fx_(IN) is the mass flow rate of the constituent x entering the reactorR.

A mathematical transformation sometimes makes it possible to make linear(additive) some variables which are not linear: for example, the meltindex of a polymer does not obey a linear mixing law but its logarithm;the abovementioned calculation of Px₁₊₂ is therefore carried out on thelogarithm of this parameter.

According to another advantageous alternative form the control method ofthe invention includes the following steps:

input of set points relating to one or more properties of the product tobe synthesized, into a master algorithm;

input of the set point of the production rate of the process into aslave algorithm;

computing of the concentration set points of the constituents in thereactor with the aid of the master algorithm, especially as a functionof the set points and of the measurements of the product properties andof measurements or predictions of the concentrations of the variousconstituents in the reactor;

transmission of the concentration set points which are calculated by themaster algorithm as input variables into the slave algorithm;

computation of flow rate set points of the constituents entering thereactor, with the aid of the slave algorithm, especially as a functionof the set point of the production rate of the process, of concentrationset points and of flow rate measurements of the constituents enteringthe reactor, and

transmission of the flow rate set points which are calculated with theaid of the slave algorithm to one or more actuators (possiblyindirectly, that is to say through the intermediacy of one or morecontrol units, e.g. PID controllers controlling the actuator(s)) inorder to control the flow rates of the constituents entering thereactor,

in which the master algorithm and/or the slave algorithm are used asdescribed above, that is to say by using the LAG function to calculatethe mass of at least one constituent in the reactor.

The master and slave algorithms are also used by means of one or severalconventional computing devices. According to an advantageous alternativeform, all of the calculations (prediction, control, and the like) ofthese two algorithms are performed by the same computing device.

Measurements of temperature (e.g. temperature in the reactor and/orentry and/or exit temperature of a possible coolant fluid) areadvantageously involved as additional variables for input into theprediction and/or control unit.

The slave algorithm preferably also takes into account the measurementsof the composition of constituents present in or leaving the reactor.

In addition, the control method advantageously includes a step ofcalculation with the aid of the slave algorithm, as a function of theflow rate measurements, of predictions of concentrations transmitted tothe master algorithm for calculating predictions of properties used asadditional input variables in the calculation of the set points ofconcentrations.

The master and slave algorithms form a control of the cascade type. Itis particularly advantageous that the master algorithm and/or the slavealgorithm should be adaptive, that is to say that some of theirparameters should be recalculated periodically (at regular or irregularintervals). Such an adaptation makes it possible especially to guaranteethat the mathematical model describes the process in its current stateas faithfully as possible, even in the event of change in some operatingconditions (temperature, pressure, production rate, and the like) and inthe event of perturbations (poisoning of the catalyst, etc.).

The master algorithm carries out the control of the properties of theproduct with the aid of a model based on characteristic equationsrelating the properties of the product to the concentrations of thevarious constituents in the reactor, as well as possibly to thetemperature prevailing in the reactor. The slave algorithm regulates theconcentrations of one or more constituents by acting on the feed flowrates of one or more constituents, which may be different.

The advantage of this "master-slave" cascade lies in the fact that themaster model determines with precision the concentrations ofconstituents which are necessary to obtain properties which are desiredfor the synthesized product, and that the slave model ensures that thevalues imposed by the master are obeyed. Being steered by the master,the slave is consequently capable:

of quickly bringing the concentrations to the values desired by themaster and maintaining them there;

of efficiently controlling the production rate of the process withoutperturbing the concentrations.

This master-slave cascade is particularly effective because both themaster and the slave take the process dynamics into account by virtue ofthe use of the LAG function in the calculations.

The slave algorithm can additionally be designed so as to supply themaster algorithm with reliable predictions of concentrations. From thesepredictions or measurements of concentrations the master algorithmdeduces reliable predictions of properties of the product which is beingsynthesized in the reactor. By comparing these predictions of propertieswith the set points of properties the master algorithm can, whereappropriate, intervene and correct the set points of concentrations.This correction is possible even before a discrepancy arises between avariable and its set point. The fact that predictions of propertiesobtained from predictions or from measurements of concentrations aretaken into account makes it possible to reduce considerably the temporalfluctuations in the properties of the synthesized product and thisresults in better consistency of the product quality.

If the properties of the product to be synthesized depend on thetemperature in the reactor(s), it is preferable to provide a temperaturecontrol by the slave algorithm. The latter sets up the heat balance ofeach reactor and, by means of the calculation of the production rate,determines the quantity of heat which must be added or removed in orderto conform to the set points of temperature which are calculated by themaster algorithm. From these results it derives input set points forheat control units of the synthesis equipment. It will be appreciatedthat this type of procedure makes it possible to intervene on the heatcontrol units of the synthesis equipment even before the temperature haschanged. Measurements of temperatures are furthermore advantageouslyinvolved as additional inputs into the slave algorithm.

The master algorithm advantageously includes the following structure:

a prediction unit based on a direct model of the process, allowing tosupply a prediction of the properties of the synthesized product as afunction of measurements and/or of predictions of the concentrations ofthe constituents;

an adaptation unit comparing the predictions of properties calculated bythe prediction unit with values actually measured on the synthesizedproduct and deriving adaptation parameters from this comparison, thesaid adaptation parameters being involved as additional inputs into thesaid prediction unit of the master algorithm; and

a control unit based on a reverse model of the process, for computing,as a function of the set points and of the predictions of properties ofthe product to be synthesized, set points of concentrations for theslave algorithm, the said adaptation parameters also being involved asadditional inputs into the said control unit.

The slave algorithm advantageously includes the following structure:

a prediction unit based on a direct model of the process allowing tosupply a prediction of the concentrations of one or more of theconstituents, based on a material balance in the reactor;

an adaptation unit comparing the predictions of concentrationscalculated by the direct model with measurements of concentration andderiving adaptation parameters from this comparison, the said adaptationparameters being involved as additional inputs into the said predictionunit of the slave algorithm; and

a control unit based on a reverse model of the process, for computing,as a function of the set point of production rate, of the set points ofconcentration which are computed by the control unit of the masteralgorithm and of the predictions of concentration which are calculatedby the prediction unit of the slave algorithm, the set points for theflow rates entering the reactor, the said adaptation parameters beinginvolved as additional inputs into the said control unit of the slavealgorithm.

The dynamics of the process are advantageously described and calculatedby means of functions of the type y=LAG (u, τ), this function being thesolution of the differential equation ##EQU3## where the arguments u andτ vary with time. The use of this function in accordance with thetheorems 1 and 2 set out below makes it possible to solve sequentiallythe material balances used by the slave algorithm and to describe theprocess kinetics using simple characteristic equations in the masteralgorithm. The LAG function further makes it possible to reduceconsiderably the volume of the calculations that are needed andconsequently makes it unnecessary to use fast and powerful computers. Inaddition, this function enables the direct and reverse models of theprocess or of some of its parts to be established in a particularlysimple manner.

The chief qualities of the proposed control can be summarized asfollows:

anticipation: the control begins to correct the measured perturbationseven before their effect on the measurements of the properties has beenseen (use of predictions of concentrations, of predictions of propertiesand of predictions of temperatures in the algorithms);

precision even in the presence of perturbations: the direct model andthe reverse model are continually recalibrated by using the measurementsof the properties (adaptation);

extended validity: the algorithm retains its validity during the changesin the production rate and grade changes, and during start-ups andstoppages (expression of the process dynamics as an equation, use ofpredictions for the variables whose measurements involve long deadtimes);

simplicity: the development and the implementation are facilitated byvirtue of an original method of expressing the process dynamics as anequation (LAG function).

The process of synthesis to be controlled is thus modelled in a formwhich is generally referred to as a "knowledge model" (first principlemodel), that is to say that its model is developed from equations whichreflect the detailed physicochemical course of the process. Such anapproach makes it possible to obtain, by means of a mathematicallyrelatively simple set of equations, results which are superior to thosethat would have been obtained by means of an empirical model of a "blackbox" type, supplying especially parameters related to real variables andbetter validity outside the identification space (extrapolation). Mostof the empirical models employ complex equations, often of a high orderif it is desired to obtain a correct simulation of the process dynamics,and in which the parameters (especially the time constants) must beidentified for a precise operating point; the model is valid only in theimmediate neighbourhood of this operating point. It is difficult togeneralize such an approach to a large number of operating points in thecase of an actual process of chemical synthesis involving manyvariables.

In contrast, according to the control method of the invention, a set ofpurely static, simple equations is employed; the process dynamics aresimulated by simple functions (cf. the LAG function above).Advantageously, the residence times (time constants of the equations)can be recalculated as often as desired, and this does not present anyproblem, given the simplicity of the equations. In the final outcome, aset of equations which are extremely simple and easy to solve in realtime, even at a high frequency, is obtained.

The proposed control method can be advantageously applied to processesof synthesis, especially continuous synthesis, of polymers(polymerization), and especially to the continuous polymerization ofolefins such as, for example, ethylene or propylene, in liquid phase aswell as in gaseous phase.

The present invention also relates to a process for the synthesis of oneor more chemical products, controlled by means of a control method inaccordance with the invention. In particular, very good results havebeen obtained in the case of the control of a process for continuoussynthesis of polyethylene by polymerization of ethylene in at least onereactor, the reactants including ethylene, hydrogen and/or an optionalcomonomer, the polymerization reaction taking place in a solvent in thepresence of a catalyst and part of the content of the reactor beingcontinuously or intermittently removed. This process can equally welltake place in liquid phase or in gaseous phase; it preferably takesplace in liquid phase (in a solvent).

The method applies in a similar manner to the synthesis of polypropylene(the chief starting monomer in this case being propylene instead ofethylene), it being also possible for propane to be present if theprocess takes place in gaseous phase. In the case of polypropylene, themelt index is often referred to as MFI instead of MI.

The invention also relates to a control device intended to implement thecontrol method for the invention, and to a plant for the synthesis ofone or more chemical products, including such a control device.

More precisely, the invention also relates to a device for controlling aprocess of synthesis of a chemical product in a synthesis equipmentincluding at least one reactor, the said device including:

at least one computing unit;

means for inputting set points of properties of the product to besynthesized into the computing unit;

means for inputting set points of production rate of the product to besynthesized into the computing unit;

units for measuring the flow rate of the flows entering the reactor;

units for measuring the composition of the flows leaving the reactor;

units for controlling flow rates (actuators) for regulating the flowrates of the flows entering the reactor;

means of communication between the said computing unit, the said unitsfor measuring flow rate and the said regulating units;

in which:

the mass of at least one constituent is calculated by the LAG functionas set out above;

the computing unit is capable of calculating with the aid of a masteralgorithm, as a function of the set points of properties, the set pointsof concentration of reactants in the reactor;

the computing unit is capable of calculating with the aid of a slavealgorithm, as a function of the set points of output and of set pointsof concentration, set points of flow rate for the flows entering thereactor, these set points of flow rate being transmitted as input setpoints to the units for controlling flow rates;

the measurements carried out by the units for measuring flow rates areinvolved as additional inputs into the said slave algorithm, to enablethe latter to calculate predictions of concentrations as a function ofthese measurements of flow rates, these predictions of concentrationsbeing involved in the master algorithm for calculating predictions ofproperties employed as additional inputs into the calculation of the setpoints of concentrations.

The invention also relates to a control device as described above, inwhich:

the synthesis equipment additionally includes:

units for heat control capable of controlling the temperature in thereactor, and

temperature sensors;

the master algorithm is capable of calculating, as a function of the setpoints of properties, set points of temperatures for the reactor;

the slave algorithm is capable of:

calculating a heat balance for the reactor,

solving this or these heat balance(s) so as to determine the heat whichmust be added to, or withdrawn from, the synthesis in order to conformto the set points of temperature, and

deriving from this or these heat balance(s) input set points for theunits for heat control of the reactor, and

receiving, as additional input variables, the measurements performed bythe temperature sensors.

The invention also relates to a device as described above, in whichmeasurements performed by the temperature sensors are involved asadditional inputs into the master algorithm.

The invention also relates to a device as described above, including:

at least one analyser capable of supplying measurements of theproperties involved in the master algorithm; and

means for inputting these measurements of properties into the computingunit;

the said computing unit including:

a first prediction unit based on a first direct model of the processpermitting the prediction of the properties of the synthesized productas a function of the predictions of concentrations calculated by theslave algorithm;

a first adaptation unit comparing the predictions of propertiescalculated by the first prediction unit with the values actuallymeasured on the synthesized product and from this comparison derivingadaptation parameters which are involved as additional inputs into thesaid first prediction unit; and

a first control unit based on a first reverse model, for calculating, asa function of the set points and of the predictions of properties, setpoints of concentrations for the slave algorithm, the said adaptationparameters also being involved as additional inputs into the said firstcontrol unit.

The invention also relates to a device as described above, additionallyincluding:

at least one analyser capable of supplying measurements of concentrationof the reactants; and

means for inputting these measurements of concentration into thecomputing unit;

the said computing unit including

a second prediction unit based on a second direct model permitting theprediction of the concentrations as a function of the material balancein the reactor;

a second adaptation unit comparing the predictions of concentrationscalculated by the second prediction unit with the measurements ofconcentration and from this comparison deriving other adaptationparameters which are involved as additional inputs into the said secondprediction unit; and

a second control unit based on a second reverse model, for calculating,as a function of the set points of output, set points of concentrationcalculated by the master algorithm and predictions of concentration fromthe second prediction unit, set points for the flow rates entering thereactor, the said other adaptation parameters involved as additionalinputs into the said second control unit.

A concrete embodiment of the invention is illustrated on the basis of aprocess for continuous synthesis of polyethylene (PE), with reference toFIGS. 1 to 10. The latter show:

FIG. 1: a diagram of a circuit for the manufacture of polyethylene;

FIG. 2: a simplified diagram of the structure of an advanced controlaccording to the invention;

FIG. 3: a basic diagram of the advanced control applied to themanufacturing circuit of FIG. 1;

FIG. 4: a basic diagram of an algorithm for adaptive control as employedin the advanced control system according to FIG. 2;

FIG. 5: a diagram of the structure of the master algorithm in theadvanced control system according to FIG. 2;

FIG. 6: a diagram of the structure of the slave algorithm in theadvanced control system according to FIG. 2;

FIG. 7: the general diagram of a control method in accordance with theinvention;

FIGS. 8-10: the diagram of particular alternative forms of the method ofthe invention.

In FIG. 7 there can first of all be seen the actual process of synthesis(Pr), which can be controlled by applying at least one set point of amanipulated variable (CGC) (for example one or more flow rates ofconstituents entering the reactor, a temperature, and the like) to asuitable actuator (valve, heating or cooling device, and the like). Thecontrol is performed by means of a control unit (OC) based on thereverse mathematical model of the process and the chief function ofwhich is to compare the set point(s) of the controlled variables (CGR)(for example one or more properties of the product to be synthesizedand/or one or more variables related to the course of the process) withthe prediction(s) of these variables (PGR). The prediction orpredictions of the controlled variables (PGR) are calculated by aprediction unit (OP) based on the direct mathematical model of theprocess, on the basis of measurements of the manipulated variables(MGC). It will be noted that no measurement of property(ies) of thesynthesized product is involved in the control.

FIG. 8 shows an alternative form of the method of FIG. 7, in which themathematical model of the process is periodically adapted by an adaptingunit (OA) on the basis of the deviation (advantageously filtered ortreated digitally) between the predictions (PGR) and the measurements(MGR) of the controlled variables. A resynchronization (shifting intime) of these measurements and of these predictions is often necessary,for example when they concern measurements of properties of thesynthesized product which take a long time to obtain. The adaptationunit (OA) transmits the results of its calculations, that is to say itsadaptation instructions, to the prediction unit (for adapting the directmodel of the process) and to the control unit (for adapting the reversemodel of the process). It will be noted that the measurement(s) ofproperty(ies) of the synthesized product are taken into account only inthe adaptation process, which generally takes place at a much lowerfrequency than the normal control process. The possible slowness ofthese measurements has therefore no direct effect on the quality of thecontrol.

FIG. 9 shows another alternative form of the invention, in which one ormore measurements of controlled variables (M_(GR)) are taken intoaccount by the control unit (OC), and one or more measurements ofcontrolled variables (M_(GR) ') (possibly different) are taken intoaccount by the prediction unit (OP). Similarly, one or more measurementsof manipulated variables (M_(GC) ') can additionally be taken intoaccount by the control unit (OC).

It is obvious that it would be possible to create another alternativeform of the method of the invention by combining the alternative formsof FIGS. 8 and 9, that is to say by using at the same time an adaptationunit and by taking into account one or more measurements of manipulatedvariables in the control unit, and/or one or more manipulated variablesin the prediction unit and/or in the control unit.

In FIG. 10 the mathematical model of the process is not adapted in theproper sense of the term, but the deviation (advantageously filtered)between the measurements and the predictions of the controlled variablesis used to correct the set points of the controlled variables (C_(GR)).In these circumstances this correction has here been shown as a simpledifference: a corrective term calculated by the adaptation unit OA(which is in fact here only a correction unit) is subtracted from eachof the set points of controlled variables, and this provides correctedset points C_(GR) ', transmitted to the control unit OC. It is obviousthat in some cases the correction may involve operations which are morecomplex than a subtraction, for example a division (in this case it ispossible, however, to return to a subtraction by considering thelogarithms of the variables considered). This method is commonly calledInternal Model Control (IMC).

If reference is made to FIG. 1, which shows diagrammatically a circuitfor continuous synthesis of polyethylene (PE), the polymerization ofethylene takes place in a loop reactor 10, in suspension in a suitablesolvent such as, for example, hexane. The process is continuous, that isto say that the reactants are injected continuously and that a part ofthe content of the reactor 10 is continuously drawn off. A circulationpump (not shown) ensures the homogeneity of the content of the reactor10.

The reactants introduced into the reactor are ethylene "Et", hydrogen"Hy" and butene "Bt" (cf. reference 11). A catalyst is also injectedcontinuously. It is important to have good control of the concentrationsof the reactants in the reactor, because the properties of the PE resinare determined chiefly by the concentration ratios Hy/Et and Bt/Et.

The polymerization temperature in the reactor is an additional parameterwhich affects the properties of the PE resin. Since the polymerizationreaction is highly exothermic, the temperature of the reactor must becontrolled by the use of a cooling circuit 12.

The reactor 10 in operation therefore contains solvent, polymer andreactants which have not yet reacted and catalyst. Its content is drawnoff continuously through the withdrawal pipe 14. This drawn-off contententers a stripper STP 16, which separates the PE polymer and the fluids(solvent and reactants). These fluids are vaporized by steam injectionand are removed into a condenser CD 18. In the latter the solvent isagain condensed before being recycled. The reactants which are lighterare separated from the solvent and are also recycled. A gas phasechromatograph GC (20) placed at the exit of the condenser 18 allows thereactant concentrations Hy/Et and Bt/Et to be determined.

The polymer removed from the stripper 16 is concentrated in acentrifuger CFG 22, and then dried in a fluidized bed drier SHLF 24,before being sent to the finishing to be granulated therein. Samples aretaken at the exit of the drier 24 in order to measure the properties ofthe resin in it: crystallinity (measured via the specific density "SD")and rheological properties (melt index (MI) or melt flow index (MFI) andmelt viscosity "μ₂ ", measured in a capillary flow under a shear of 100s⁻¹).

The dynamics of this PE synthesis process are slow and complex:

The loop reactor 10 behaves as a perfectly mixed reactor. Consequently,any change in the feed flow rate of one of the reactants will bereflected only gradually in the concentration of this reactant in thereactor. This is because the new flow rate must be mixed with the entirevolume of the reactor 10 in order to bring it to the new equilibriumconcentration.

The measurement of the concentrations of the reactants is done by a gasphase chromatograph 20; this is a noncontinuous instrument which worksin successive steps: taking a sample of gas, analysis and thenderivation of the results. There is therefore a dead time (from 5 to 15min) between the changes in concentration and their measurement.

The properties of the polymer manufactured at any instant depend chieflyon the concentrations of the reactants. Any change in theseconcentrations therefore instantly affects the properties of the polymermanufactured. On the other hand, the average properties in the reactorchange only gradually because the freshly produced polymer must mix withthe polymer already present in the reactor 10 (residence time: ±2 h).

When the polymer is drawn off from the reactor 10, it again undergoes aseries of mixings in the various units of equipment (STP, CFG and SHLF)intended to dry it (residence time: ±2 h). Samples of polymer are thentaken and analysed by the works laboratory. The results of theseanalyses will therefore be communicated to the manufacturer only after anew dead time, which may be considerable (±2 h).

Modelling of the Process with the Aid of an LAG Function

According to the method of the invention the dynamic modelling of aprocess of continuous synthesis is carried out by resorting toassumptions of perfect mixings and of pure delays. The perfect mixingsare expressed as an equation by means of a function which is well knownto engineers, the "LAG" function, or low-pass filter (of the 1st order);this function is linear and easily programmable. It is defined asfollows: y=LAG (u, τ) (known as "LAG of u during τ") as being thesolution of the differential equation ##EQU4## in which the arguments uand τ vary with time.

This equation can be solved numerically (even in real time) by analgebraic equation of the 1st order, which has the following variablesas arguments:

the sampling period "T" (or time elapsed since the last iteration)

the residence time (or time "constant") "τ" at the instant "t"

the state variable "y" at the preceding instant "t-T"

the control variable "u" at the present instant "t" (u and τ in factrepresent the values measured or calculated at the instant "t" on thevariables "u" and "τ", which are assumed to have been constantthroughout the preceding interval "T").

T is preferably small in relation to τ (for example at least 10 timessmaller), so as to increase the precision of the calculation.

The solution of the abovementioned equation can be calculated, forexample, by the following formula:

    y(t)=y(t-T)·e.sup.-T/τ(t) +u(t)·(1-e.sup.-T/τ(t))

or else, more simply (approximately): ##EQU5##

The modelling of the process with the aid of the LAG function is basedon the following theorems:

Let there be a perfectly mixed reactor (CSTR) of volume V_(R). It is fedwith various constituents (reactants or inerts), including the reactant"x" (entry flow rate FX_(IN)) which has the property "Px_(IN) " at theentry. The exit flow rate "F_(OUT) " (draw-off) is also measured.

Theorem 1

Application of the LAG method to the calculation of a mass balance:

At each instant the mass "Mx_(R) " of a constituent "x" in a perfectlymixed reactor (CSTR) is equal to the LAG of the product of the entrymass flow rate "Fx_(IN) " multiplied by a time "τ_(X) ", during thissame time "τ_(X) ":

    Mx.sub.R =LAG(Fx.sub.IN ·τ.sub.X, τ.sub.X)(in kg)

The time "τ_(X) " is the "residence time of "x"; its value is the massof the constituent Mx_(R), divided by the sum of the "leaving" mass flowrates (quantity consumed by the reaction "FRx", flow rate leaving thereactor "Fx_(OUT) ", and so on).

    τ.sub.X =Mx.sub.R /Fx.sub.OUT +FRx+etc.)(in h)

This theorem thus gives an accurate method for the dynamic calculation(even in real time) of the concentrations in a perfectly mixed reactor.In fact, if "V_(R) " is the reactor volume, the concentration "Cx_(R) "of the constituent "x", expressed in kg/m³, has the value

    Cx.sub.R =Mx.sub.R /V.sub.R (in kg/m.sup.3)

Since the total volume flow rate "FV_(OUT) " leaving the reactor isknown, the residence time of the reactor "τ_(R) " is defined:

    τ.sub.R =V.sub.R /FV.sub.OUT

Hence, the mass flow rate "Fx_(OUT) " of the constituent "x" leaving thereactor (draw-off) is:

    Fx.sub.OUT =Mx.sub.R /τ.sub.R

It will be noted that if "x" is an inert (which does not undergoreaction and leaves the reactor only by draw-off), this gives:

    τ.sub.X =τ.sub.R

Furthermore, in the frequent case where the rate of reaction of "x" isproportional to its concentration Cx_(R), with a proportionality factorR_(X), this gives: FRx=R_(X) ·Mx_(R) and hence

    τ.sub.X =1/(R.sub.X +1/τ.sub.R)

Theorem 2

Application of the LAG method to the calculation of a property of amixture:

Let there be a property "Px" of a constituent, obeying the linear mixinglaw:

    Px.sub.1+2 =w.sub.1 ·Px.sub.1 +w.sub.2 ·Px.sub.2

where w₁ and w₂ are the mass fractions of property Px₁ and Px₂ (with w₁+w₂ =1).

At each instant the property Px_(R) in a perfectly mixed reactor (CSTR)is equal to the LAG of the property at the entry Px_(IN), during aresidence time which has the value of the mass ratio Mx_(R) of theconstituent in the reactor divided by the entering mass flow rate(and/or appearing by reaction) Fx_(IN) :

    Px.sub.R =LAG(Px.sub.IN, Mx.sub.R /Fx.sub.IN)

It is thus possible to take the dynamics of the process into account andto recalculate its time constants continuously.

As explained above, the "properties" which are involved here can in somecases have undergone a mathematical transformation which makes themlinear (for example the logarithm of the melt index of a polymer can beconsidered as obeying a linear mixing law).

Principle of the Control

When the model of the process of synthesis has been established, analgorithm is required which calculates the parameters necessary for thecontrol of this process.

FIG. 2 shows a simplified general diagram of the type of advancedcontrol (Advanced Process Control or "APC") adopted for thepolymerization process described above. It is seen that this controlsystem includes a cascade of two algorithms, this cascade steeringespecially the PID controllers of the reactant feed flow rates.

The two algorithms in cascade, also called master algorithm and slavealgorithm, are both adaptive dynamic algorithms based on modelsoriginating from the knowledge of the process, (in contrast to empiricalmodels), which are based especially on the material balances and thekinetics of the controlled process. They employ the predefined LAGfunction.

In FIG. 3, which shows the principle of the control system in thecontext of the polymerization process described above, it is seen that:

the master algorithm is based on the characteristic equations of thecatalysts, that is to say equations which give the properties of the PEas a function of the polymerization temperature and of theconcentrations of the reactants in the reactor; it provides the slavealgorithm with the set points of the concentrations of reactants tosatisfy the set points for the properties of the PE;

the slave algorithm is based on a material balance and the chemicalkinetics of the reactions; it provides the feed flow rate controllerswith the set points of flow rates of reactants which are necessary tosatisfy the set points of concentrations imposed by the master algorithmand the set point of the production rate of the process. Preferably italso calculates an anticipative ("feed-forward") term for the set pointof temperature, improving the temperature control during changes inproduction rate.

This type of control is perfectly precise only if the model is perfectand takes into account all the possible perturbations. In general thisis not the case. This is why in general (see FIG. 4) the direct model(and the reverse model) is continuously adapted by comparing thepredictions with the measurements of the properties. This "adaptation"of the model allows its precision to be maintained in the presence ofperturbations which are not modelled and thus makes it possible toobtain a more precise control in all circumstances.

The Slave Algorithm

FIG. 6 illustrates the principle of the slave algorithm:

1. a prediction unit using a direct model of the predicted process, fromthe measurements of the flow rates feeding the reactor and the reactantand polymer concentrations;

2. an adaptation unit compares the concentrations of ethylene (Et),hydrogen (Hy) and butene (Bt) measured by an analyser (gaschromatograph) with the values predicted by the direct model, so as todetermine three adaptation parameters:

the specific activity of the catalyst for ethylene "AEt", in kg/h ofpolyethylene per kg of catalyst and per kg/m³ of ethylene

the gain error in the measurement of flow rate of hydrogen "KfHy"

the purity of the butene feed "KfBt";

3. the control unit calculates the set points for the feed flow rates ofthe reactants, from set points of concentration calculated by the masteralgorithm and from the set point of production rate; these set points offlow rate are made up of a feed-forward based on the reverse model andof a feedback proportional to the deviation between the direct model andthe set points of concentration.

To understand the calculations performed by the slave algorithm, in thecase of a process for the synthesis of polyethylene, it must be knownfirst of all that it is generally accepted that the rate ofpolymerization "VitP_(Et) " is proportional:

to the concentration of unpolymerized Et cEt_(R) (in kg/m³),

to the concentration of active catalyst in the reactor cCA_(R) (inkg/m³), and

to a proportionality factor, a function (which is difficult to quantify)of the temperature, of the concentrations of Hy, of Bt and ofcocatalyst, of the presence of poisons, and the like. This term iscalled "catalytic activity" for ethylene A_(Et). In the absence of amajor malfunction, (poison, and the like), it varies relatively littlein the course of a campaign.

    VitP.sub.Et =A.sub.Et ·cCA.sub.R ·cEt.sub.R (kg/m.sup.3 h)

If V_(R) is the volume of the reactor, the quantity of ethylene "FpEt"which polymerizes in the reactor at each unit of time ("polymerizationflow rate") is therefore: ##EQU6## where MEt_(R) is the mass of ethylenein solution in the reactor (in kg).

It is known furthermore that the rate of incorporation of Hy isapproximately 100 times slower than that of Et and 10 times slower forBt. This gives:

    FpHy=A.sub.Et ·cCA.sub.R ·MHy.sub.R /100

    FpBt=A.sub.Et ·cCA.sub.R ·MBt.sub.R /10

where MHy_(R) is the mass of hydrogen in solution in the reactor (in kg)and

MBt_(R) is the mass of butene in solution in the reactor (in kg).

The slave model now uses the following measurements:

FEt_(IN) =ethylene (monomer) feed flow rate (kg/h)

FSv_(IN) =solvent (hexane) feed flow rate (kg/h)

FCA_(IN) =catalyst feed flow rate (kg/h)

FHy_(IN) =hydrogen (transfer agent) feed flow rate (kg/h)

FBt_(IN) =butene(comonomer) feed flow rate (kg/h)

It also uses the following adaptation parameters:

A_(Et) ="catalytic activity" for ethylene

KfHy=gain error in the measurement of the hydrogen feed

KfBt=purity of the butene feed.

The following calculations are performed sequentially, in the followingorder, at a high frequency (the time interval separating each iterationbeing small in relation to the shortest of the residence times τ_(x)).

Since the reactor volume is constant, the leaving flow rate per unitvolume is equivalent to the entering flow rate per unit volume(noncompressible fluids). The leaving flow rate per unit volume"Fv_(OUT) " can therefore be calculated as the sum of the entering massflow rates divided by the density which they have in the reactor

    FV.sub.OUT =FSv.sub.IN /650+FEt.sub.IN /950+FBt.sub.IN /600 (m.sup.3 /h)

(where the densities are the following: 650 kg/m³ for the solvent, 950kg/m³ for the polyethylene, 600 kg/m³ for butene). It is assumed herethat all the ethylene is instantly converted to polyethylene and theflow rate of hydrogen and of catalyst (a few kg) is ignored.

The solvent is chemically inert and leaves the reactor only by beingdrawn off from the reactor. Its mass "MSv_(R) " in the reactor iscalculated by employing theorem 1:

    τ.sub.R =V.sub.R /FV.sub.OUT (h) (residence time in the reactor)

    MSv.sub.R =LAG(FSv.sub.IN ·τ.sub.R, τ.sub.R) (kg)

The catalyst is deactivated with a time constant "kd"; the mass "MCA_(R)" of the active catalyst in the reactor is calculated as follows:

    τ.sub.CA =1/(1/τ.sub.R +kd) (h)

    MCA.sub.R =LAG(FCA.sub.IN ·τ.sub.CA, τ.sub.CA) (kg)

and therefore the concentration "cCA_(R) " of active catalyst in thereactor is:

    cCA.sub.R =MCA.sub.R /V.sub.R (kg/m.sup.3)

Ethylene "leaves" the reactor in the draw-off flow and in thepolymerization reaction. Its mass in the reactor "MEt_(R) " iscalculated as follows:

    τ.sub.Et =1/(1/τ.sub.R +A.sub.Et ·cCA.sub.R) (h)

    MEt.sub.R =LAG(FEt.sub.IN ·τ.sub.Et, τ.sub.Et) (kg)

The "raw" (uncalibrated) mass of hydrogen in the reactor "MHy_(RAW) " iscalculated similarly:

    τ.sub.Hy =1/(1/τ.sub.R +A.sub.Et ·cCA.sub.R /100) (h)

    MHy.sub.RAW =LAG(FHy.sub.IN ·τ.sub.Hy, τ.sub.Hy) (kg)

The mass "MHy_(R) ", corrected to take into account the gain error inthe measurement of the hydrogen feed, is:

    MHy.sub.R =KfHy·MHy.sub.RAW (kg)

The ratio Hy:Et in the reactor is therefore:

    HyEt.sub.R =MHy.sub.R /MEt.sub.R

The mass of "raw" butene "MBt_(RAW) " is calculated similarly:

    τ.sub.Bt =1/(1/τ.sub.R +A.sub.Et ·cCA.sub.R /10) (h)

    MBt.sub.RAW =LAG(FBt.sub.IN ·τ.sub.Bt, τ.sub.Bt) (kg)

The mass "MBt_(R) ", corrected to take into account the purity of thebutene feed, is:

    MBt.sub.R =KfBt·MBt.sub.RAW (kg)

The ratio Bt:Et in the reactor is therefore:

    BtEt.sub.R =MBt.sub.R /MEt.sub.R

As already shown, the polymerization flow rate "FpEt" (instantaneousproduction rate) is:

    FpEt=A.sub.Et ·cCA.sub.R ·MEt.sub.R (kg/h)

Since the polymer is inert and does not undergo reaction, its mass inthe reactor "MPE_(R) " is:

    MPE.sub.R =LAG(FpEt·τ.sub.R, τ.sub.R) (kg)

The flow rate of polymer leaving the reactor "FPE_(OUT) " is therefore:

    FPE.sub.OUT =MPE.sub.R /τ.sub.R (kg/h)

Adaptation of the Slave Model

The adaptation block employs an analyser (for example a gaschromatograph "GC") to obtain the measurements for the concentrations inthe reactor of ethylene "cEt_(GC) ", of hydrogen "cHy_(GC) " and ofbutene "cBt_(GC) " (expressed, for example, in kg/m³). Thesemeasurements are compared with the values predicted by the direct modelin order to determine the following three adaptation parameters:

the specific activity of the catalyst for ethylene "AEt", in kg/h ofpolyethylene per kg of catalyst and per kg/m³ of ethylene

the gain error in the measurement of hydrogen flow rate "KfHy"

the purity of the butene feed "KfBt".

The gas chromatograph supplies sampled measurements with a delay ofapproximately 6 minutes.

The calculation of the specific activity for ethylene "AEt" ensues fromthe following equalities: ##EQU7##

Since the measurement cEt_(GC) is sampled and noisy, it is undesirableto find it in a LEAD; it is therefore preferable to employ:

    A.sub.et '=LAG(A.sub.Et ", τ.sub.Et)≈LAG(FEt.sub.IN /cCA.sub.R, τ.sub.Et)/(cEt.sub.GC ·V.sub.R)-1/LAG(τ.sub.R ·cCA.sub.R, τ.sub.Et)

Account is taken of the delay of 6 minutes in the measurement ofcEt_(GC) by introducing two LAGs in series of 3 minutes each into thevalues of the model, and the final formula is obtained:

    A.sub.et =LAG(FEt.sub.IN /cCA.sub.R, τ.sub.Et, 3/60, 3/60)/(cEt.sub.GC ·V.sub.R)-1/LAG(τ.sub.R ·cCA.sub.R, τ.sub.Et, 3/60, 3/60)

The calculation of the gain in the hydrogen flow rate "KfHy" ensues fromthe following equalities: ##EQU8##

Account is taken of the delay of 6 minutes in the measurement ofcHy_(GC) by introducing two LAGs in series of 3 minutes each into thevalue of the model, and the final formula is obtained:

    KfHy=cHy.sub.GC ·V.sub.R /LAG(MHy.sub.RAW, 3/60, 3/60)

In the same way as for KfHy, the correction parameter is calculated forthe butene purity "KfBt":

    KfHy=cBt.sub.GC ·V.sub.R /LAG(MBt.sub.RAW, 3/60, 3/60)

The control algorithm has, as inputs:

the set points of concentration which are calculated by the masteralgorithm; more precisely, the set points for the concentration ratioscHy_(R) /cEt_(R) "HyEt_(SP) " and cBt_(R) /cEt_(R) "BtEt_(SP) " (inkg/kg)

the set point for the production rate of the process FpEt_(SP), fixed bythe operator

the set point for the ethylene concentration cEt_(SP), fixed by theoperator;

the concentrations calculated by the model.

It calculates the set points for the feed flow rates of the reactantsFEt_(SP), FCA_(SP), FHy_(SP) and FBt_(SP). Various algorithms can beused, including the MBPC (Model Based Predictive Control). They can ingeneral be found to be composed of a feed-forward based on the reversemodel and a feedback proportional to the deviation between the directmodel and the set points of concentration.

Control of the Ethylene Feed

Feed-forward: value for maintaining the current concentration, based onthe inversion of the stationary value of the following equation:

    MEt.sub.R =LAG(FEt.sub.IN ·τ.sub.Et, τ.sub.Et)FEt.sub.FF =MEt.sub.R /τ.sub.Et (kg)

Feedback: proportional to the deviation between the set point cEt_(SP)and the model

    FEt.sub.FB =5·(cEt.sub.SP ·V.sub.R -MEt.sub.R)

Set point:

    FEt.sub.SP =FEt.sub.FF +FEt.sub.FB

Control of the Catalyst Feed

Feed-forward: value for maintaining the current concentration, based onthe inversion of the stationary value of the following equation:

    MCA.sub.R =LAG(FCA.sub.IN ·τ.sub.CA, τ.sub.CA)FCA.sub.FF =MCA.sub.R /τ.sub.CA (kg)

Feedback: proportional to the deviation between the set point FpEt_(SP)and the model, according to the following formula:

    FpEt=A.sub.Et ·MEt.sub.R ·MCA.sub.R /V.sub.R FCA.sub.FB =5·(FpEt.sub.SP /(A.sub.Et ·MEt.sub.R /V.sub.R)-MCA.sub.R)

Set value:

    FCA.sub.SP =FCA.sub.FF +FCA.sub.FB

Control of the Hydrogen Feed

Feed-forward: value for maintaining the current concentration, based onthe inversion of the stationary value of the following equation:

    MHy.sub.R =LAG(FHy.sub.IN ·τ.sub.Hy, τ.sub.Hy)FHy.sub.FF =MHy.sub.RAW /τ.sub.Hy (kg)

Feedback: proportional to the deviation between the set point of ratioHyEt_(SP) and the model.

    FHy.sub.FB =5·(HyEt.sub.SP ·MEt.sub.R -MHy.sub.R)

Set value:

    FHy.sub.SP =FHy.sub.FF +FHy.sub.FB

Control of the Butene Feed (Similar to Hydrogen) ##EQU9##

The equations which precede summarize the equations of the slavealgorithm. They are performed every 10 seconds by the digital controland command system (SNCC).

The Master Algorithm

FIG. 5 illustrates the principle of the master algorithm:

1. its prediction unit (based on a direct model) predicts the chiefproperties of the polymer (MI and SD); for this purpose it uses themeasurement of the polymerization temperature, the predictions for theconcentrations in the reactor which are supplied by the slave model andthe residence times of the PE in the various units of equipment;

2. its adaptation unit compares the measurements of MI and SD, which areperformed (also on leaving the drier) either by the measurementlaboratory every 2 h or by a continuous analyser, with the valuespredicted by the direct model, so as to determine the 2 adaptationparameters, which are corrective parameters, multiplicative in the caseof the MI and additive in the case of the SD;

3. its control unit (based on a reverse model) calculates the set pointsfor the concentrations in the reactor (ratios Hy:Et and Bt:Et) from theset points of MI and of SD supplied by the operator. As in the case ofthe slave algorithm, this calculation is made up of a feed-forward basedon the direct model and of a feedback proportional to the deviationbetween the direct model and the operator's set points.

For a given catalyst the properties of the resins in a steady state arefunctions of the polymerization temperature and of the concentrations ofthe reactants. Among the various static equations which are taught inthe literature, the following equations have been chosen:

    log(MI)=a.sub.0 +a.sub.1 ·T°+a.sub.2 ·log(Hy/Et)+a.sub.3 ·Bt/Et

    SD=b.sub.0 +b.sub.1 ·T°+b.sub.2 ·(Bt/Et).sup.b3 +b.sub.4 ·log(MI).

The parameters a₀ to a₃ and b₀ to b₄ are obtained by identification in asteady state, for a number of resins manufactured with the samecatalyst.

Furthermore, the various units of equipment encountered by thepolyethylene until the time when its properties are measured (reactor,stripper, centrifuge and then drier) can all be assimilated to, as afirst approximation, perfectly mixed reactors.

The master algorithm uses the following measurements as inputs:##EQU10## and the following calculations carried out by the slavealgorithm: FpEt=instantaneous output of polymer (production rate) (kg/h)

FPE_(OUT) =flow rate of PE leaving the reactor (kg/h) ##EQU11##

The raw instantaneous values (before adaptation) of the SD and of thelogarithm of the MI ("lMI") are calculated by:

    SD.sub.INS =b.sub.0 +b.sub.1 ·T.sub.R +b.sub.2 ·(BtEt.sub.R).sup.b3 +b.sub.4 ·lMI.sub.INS

    lMI.sub.INS =a.sub.0 +a.sub.1 ·T.sub.R +a.sub.2 ·log(HyEt.sub.R)+a.sub.3 ·BtEt.sub.R

The raw average properties at the reactor exit are calculated byemploying theorem 2:

    lMIr=LAG(lMI.sub.INS, MPE.sub.R /FpEt)

    SDr=LAG(SD.sub.INS, MPE.sub.R /FpEt)

In effect:

the properties lMI and SD correspond quite well to a linear law ofmixtures

the loop reactor may be assimilated to a perfectly mixed reactor

the mass flow rate of PE "entering" (appearing in) the reactor iseffectively FpEt, the quantity of PE which polymerizes at any instant(production rate).

Raw properties at the measurement: since it is known that there areapproximately 500 kg of PE per m³ in the stripper, and if it is assumedthat the stripper is a perfectly mixed reactor, the raw properties atthe stripper exit are calculated as follows:

    lMIstp=LAG(lMIr, 500·Vstp/FPE.sub.OUT)

    SDstp=LAG(SDr, 500·Vstp/FPE.sub.OUT)

Since the residence time in the centrifuge is very short, it can beignored.

The drier is a fluidized bed drier; it continuously containsapproximately 1400 kg of PE. It can be assumed that the level in thestripper does not change much and that the flow leaving it is equal tothat which enters it. Hence, the flow rate of PE entering the drier isFPE_(OUT). At the exit of the drier, the place where the sample is takenfor the property measurement, there are then the following raw values:

    lMIsh=LAG(lMIstp, 1400/FPE.sub.OUT)

    SDsh=LAG(SDstp, 1400/FPE.sub.OUT)

The properties after adaptation are obtained by involving the adaptationparameters kMI (multiplicative parameter) and kSD (additive parameter);the reactor exit, stripper and drier properties after adaptation aretherefore:

    MIr.sub.C =kMI·10.sup.lMIr

    SDr.sub.C =kSD+SDr

    MIstp.sub.C =kMI·10.sup.lMIstp

    SDstp.sub.C =kSD+SDstp

    MIsh.sub.C =kMI·10.sup.lMIsh

    SDsh.sub.C =kSD+SDsh

Adaptation of the Master Algorithm

Measurements of properties take a certain time to be carried out (±5 minif in-line analyser, ±1 h if performed by the laboratory). To enable theadaptation parameters to be calculated it is therefore necessary toresynchronize (shift in time) the raw predictions from the model withthe measurements. This can be done, for example, by means of a shiftregister (here called "DELAY function"):

    lMI.sub.DEL =DELAY (lMIsh, τ.sub.MI)

    SD.sub.DEL =DELAY (SDsh, τ.sub.SD)

with τ_(MI) and τ_(SD) =±5 min or ±1 h, according to whether themeasurement is carried out by a continuous analyser or by thelaboratory.

At each new measurement of MI or of SD the raw adaptation parameter kMI'or kSD' is recalculated by comparing the resynchronized raw model valuewith the measured value:

    kMI'=log(MI.sub.MES)-lMI.sub.DEL

    kSD'=SD.sub.MES -SD.sub.DEL

These raw values are filtered in order to attenuate the rapid reactionswhich the possible perturbations (noise) of measurements might inflicton the process:

    kMI=LAG(kMI', ±1 h)

    kSD=LAG(kSD', ±1 h)

Control Unit

The control unit has as set points the values MI_(SP) and SD_(SP),entered by the operator. He calculates the set points for the ratios ofthe concentrations in the reactor HyEt_(SP) and BtEt_(SP) needed toobtain rapidly the desired properties MI_(SP) and SD_(SP). Thiscalculation is done in 2 steps:

1. from the set points MI_(SP) and SD_(SP) supplied by the operator, andfrom the values after adaptation of the MI and of the SD in the variousunits of equipment, the control unit calculates the set points MIi_(SP)and SDi_(SP) for the instantaneous output. These instantaneous setpoints are made up of a feed-forward and of a feedback proportional tothe deviation between the direct model and the operator's set points;

2. the set points for the concentration ratios HyEt_(SP) and BtEt_(SP)are then calculated by inverting the static equation used above for thecalculation of the instantaneous value of the MI and of the SD.

Set points for the instantaneous properties: the drier exit propertiesare compared with the set points of properties, to determine the desiredset points for the properties at the stripper exit (the centrifuge isignored):

    MIstp.sub.SP =10.sup.(log(MISP)+0.1 ·log(MISP)-log(MIshC)))

    SDstp.sub.SP =SD.sub.SP +0.1·(SD.sub.SP -SDsh.sub.C)

Similarly, the desired set points at the reactor exit are calculatedfrom the deviation between these stripper exit set points and thecalibrated values at the stripper:

    MIr.sub.SP =10.sup.(log(MIstpSP)+0.5·(log(MIstpSP)-log(MIstpC)))

    SDr.sub.SP =SDstp.sub.SP +0.5·(SDstp.sub.SP -SDstp.sub.C)

Finally, the desired set points for the instantaneous output arecalculated from the deviation between these reactor exit set points andthe corresponding calibrated values:

    MIi.sub.SP =10.sup.(log(MIrSP)+2·(log(MIrSP)-log(MIrC)))

    SDSi.sub.SP =SDr.sub.SP +2·(SDr.sub.SP -SDr.sub.C)

Set points for the concentration ratios: the set points for theconcentration ratios HyEt_(SP) and BtEt_(SP) are obtained by invertingthe static equation used above for the calculation of the instantaneousvalue of the MI and of the SD, by substituting in the MI and SD termsthe desired set points for the instantaneous output and by applying theadaptation parameter.

Starting from:

    log(MIi.sub.SP /kMI)=a.sub.0 +a.sub.1 ·T.sub.R +a.sub.2 ·log(HyEt.sub.SP)+a.sub.3 ·BtEt.sub.R

    SDi.sub.SP -kSD=b.sub.0 +b.sub.1 ·T.sub.R +b.sub.2 ·(BtEt.sub.SP).sup.b3 +b.sub.4 ·lMI.sub.INS

one obtains:

    a.sub.2 ·log(HyEt.sub.SP)=log(MIi.sub.SP /kMI)-(a.sub.0 +a.sub.1 ·T.sub.R +a.sub.3 ·BtEt.sub.R)

which gives:

    HyEt.sub.SP =10.sup.((log(MIiSP/kMI)-a0-a1·TR-a3·BtEtR)/a2)

and

    b.sub.2 ·(BtEt.sub.SP).sup.b3 =SDi.sub.SP -kSD-(b.sub.0 +b.sub.1 ·T.sub.R +b.sub.4 ·lMI.sub.INS)

which gives:

    BtEt.sub.SP =((SDi.sub.SP -kSD-b.sub.0 -b.sub.1 ·T.sub.R -b.sub.4 ·lMI.sub.INS)/b.sub.2).sup.1/b3

The above equations summarize the equations of the master algorithm.They are performed every 30 seconds by the SNCC.

With this process it is possible to control the polymerization withgreat precision. In particular:

the controlled properties (MI and SD) are maintained as near as possibleto the desired values, with a minimal scatter

the changes of grade (and hence of the MI and SD properties) are carriedout with speed and precision

polymerization start-ups and stoppages, as well as the changes in theproduction rate of the process, are carried out in a more speedy manner,while the MI and the SD are maintained very near the desired values.

Although the control method according to the invention has beenpresented with the aid of a process for the synthesis of polyethylene bycontinuous polymerization of ethylene, it is to be understood that thiscontrol method will be generally effective for other processes ofsynthesis, and in particular for the processes exhibiting one or more ofthe following characteristics:

a multivariable control is necessary because a number of variablesaffect the set of the properties to be regulated;

the process dynamics are slow: mixings in series, long dead times;

the measurements of the properties are sampled at a low frequency and/orare noisy;

the control must be dynamic, that is to say valid regardless of theproduction rate of the process, as well as during the changes in theproduction rate and in the grade (properties) of the product to besynthesized;

it is advantageous to estimate some variables which are not measureddirectly.

To be capable of being easily implemented with the techniques presented,it suffices that:

the static equations of the process are known (they are often known atleast in a certain measure, otherwise the process could not becontrolled);

the process dynamics can be approached using perfect mixtures and deadtimes;

the necessary measurements are available and of sufficient quality (inparticular the flow rates of the reactants and the flow rates passingthrough the storage vessels concerned).

The particular use of the LAG function described above, especially intheorems 1 and 2, can naturally be extended to control methods based ona structure other than that which has been set out, which includes amaster algorithm and a slave algorithm which are different. It can, forexample, be applied in a controlled method comprising only a singlealgorithm.

EXAMPLES

8 trials of synthesis of polyethylene (PE) of 4 different types (definedby the MI, SD, etc.) were carried out, by using a conventional controlmethod and by using the method of the invention, respectively. The tablebelow summarizes the findings which were made on the basis of manymeasurements of the melt index of the 8 polymers obtained. Cpk denotesthe centred capability value of the process.

    ______________________________________                                                                     Control according to                                       Conventional control                                                                             the invention                                              Standard           Standard                                         PE type   deviation                                                                              Cpk       deviation                                                                            Cpk                                       ______________________________________                                        1         0.127     0.909    0.059   2.202                                    2         --       0.61      --     2.0                                       3         --       0.48      --     1.88                                      4         --       0.64      --     1.09                                      ______________________________________                                    

It is found that the capability value Cpk is more than doubled by virtueof the use of the method of the invention, which shows that theproperties are approximately half as scattered and/or better-centred inrelation to the set points imposed.

    ______________________________________                                        Table of the abbreviations employed                                           ______________________________________                                        a.sub.I  parameters for the static equation of the MI                                  (I = 0 to 3)                                                         b.sub.I  parameters for the static equation of the SD                                  (I = 0 to 4)                                                         A.sub.Et catalytic activity for ethylene (m.sup.3 kg.sup.-1 h-1)              CX.sub.GC                                                                              concentration of "x" obtained by measurement                                  from the analyser (kg/m.sup.3)                                       cx.sub.R concentration of "x" in the reactor (kg/m.sup.3)                     cx.sub.SP                                                                              set point for the concentration of "x" in the                                 reactor (kg/m.sup.3)                                                 Fpx      mass flow rate of polymerization of "x"                                       (production rate) (kg/h)                                             FV.sub.OUT                                                                             volume flow rate leaving the reactor (m.sup.3 /h)                    Fx.sub.IN                                                                              mass flow rate of "x" entering (kg/h)                                Fx.sub.OUT                                                                             mass flow rate of "x" leaving (kg/h)                                 kd       deactivation constant of the catalyst (l/h)                          KfBt     corrective (adaptation) parameter for butene                         KfHy     corrective (adaptation) parameter for hydrogen                       kMI      corrective (adaptation) parameter for the MI                         kSD      corrective (adaptation) parameter for the SD                         LAG (,)  low-pass filter function of the 1st order                            MI.sub.MES                                                                             measurement of the MI (Melt Index)                                   MIy      raw (uncalibrated) MI in "y"                                         MIy.sub.c                                                                              calibrated MI (with adaptation) in "y"                               MIy.sub.SP                                                                             (calibrated) set point of MI for "y"                                 SD.sub.MES                                                                             measurement of the SD (standard density)                             SD.sub.y raw (uncalibrated) SD (standard density) in "y"                      SDy.sub.c                                                                              calibrated SD (with adaptation) in "y"                               SDy.sub.SP                                                                             (calibrated) set point of SD for "y"                                 Mx.sub.RAW                                                                             raw (uncalibrated) mass of "x" in the reactor (kg)                   Mx.sub.y calibrated mass of "x" (with adaptation) in "y" (kg)                 R.sub.X  reactivity of X in the reactor                                       V.sub.Y  volume of "y" (m.sup.3)                                              τ.sub.R                                                                            residence time in the reactor (h)                                    τ.sub.X                                                                            residence time for "x" in the reactor (h)                                     "x" can represent the following constituents:                        Bt       butene                                                               CA       catalyst                                                             Et       ethylene                                                             Hy       hydrogen                                                             Sv       solvent                                                                       "y" can represent the following units of                                      equipment:                                                           r        polymerization reactor                                               stp      stripper                                                             sh       drier (fluidized bed)                                                ______________________________________                                    

    ______________________________________                                        Legend of the FIGS.                                                           ______________________________________                                        10       polymerization reactor                                               11       feed of reactants (raw materials), catalyst,                                  solvent                                                              12       coolant circuit                                                               withdrawal pipe                                                      16       stripper                                                             18       condenser                                                            20       9as phase chromatograph                                              22       centrifuger                                                          24       fluidized bed drier                                                  25       solvent and reactants to be recycled                                 26       polyethylene                                                         27       reactants to be recycled                                             28       solvent to be recycled                                               30       set points of the polymer property                                   31       set points of the process production rate                            32       master algorithm                                                     33       slave algorithm                                                      34       concentration set points                                             35       entry flow set points                                                36       controllers (PID) for the flow rates                                 37       measurements                                                         38       temperature control                                                  39       temperature feed-forward                                             40       polymerization dynamics: chemical kinetics and                                material balance                                                     41       simulations of the production rate and of the                                 ratios Hy/Et and Bt/Et                                               42       measurements of temperature, of flow rates and of                             concentrations                                                       43       controlled process                                                   44       analysis of a sample of the product synthesized by                            the process                                                          51       measurement of quantities related to the course of                            the process                                                          52       measurement of the polymer properties                                53       direct model; prediction of the properties at the                             measurement                                                          54       comparison: calibration of the model (adaptation)                    55       control algorithm based on the reverse model                                  (feed-forward + feedback)                                            56       set points for the variables related to the                                   process                                                              57       measurements and set points of entry flow rates                      58       measurement of the temperature and prediction of                              the concentrations                                                   59       direct model: equations of the properties as a                                function of the concentrations                                       60       prediction of the properties                                         61       set points for the concentrations in the reactor                     62       measurement of the entry flow rates                                  63       measurement of the concentrations in the reactor                     64       direct model; prediction of the concentrations                                based on the material balance                                        65       concentration predictions                                            66       comparison; calculation of the adaptation                                     parameters                                                           ______________________________________                                    

What is claimed is:
 1. A control method for synthesis of at least onechemical product in an apparatus comprising at least one reactor (R), inwhich one or more manipulated variables (GC) is allowed to act on thecourse of the process in order to make one or more controlled variables(GR) related to the properties of the product and/or to the course ofthe process, equal to corresponding set points (C_(GR)), said methodcomprising:(a) inputting set points concerning the controlled variables(C_(GR)); (b) computing, by means of a prediction unit (OP), predictionsof the controlled variables (P_(GR)), based on measurements of theprocess manipulated variables (M_(GC)); (c) using a control unit (OC) tocompute the set points of the process manipulated variables (C_(GC)),based on the set points (C_(GR)) and the predictions (P_(GR)) of thecontrolled variables; (d) transmitting the set points of the processmanipulated variables (C_(GC)) to actuators, in order to act on thecourse of the process;wherein the prediction unit (OP) is based on amathematical model of the process (M); and wherein the prediction unit(OP) is designed in such a way that the mass M_(XR) of at least oneconstituent (X) in the reactor (R) is predicted by the equation:

    M.sub.XR =LAG(F.sub.XRin ·τ.sub.X, τ.sub.x)

in which: F_(XRin) is the mass flow rate of the constituent X enteringthe reactor R; τ_(X) is the residence time of X in the reactor, thevalue of which is

    τ.sub.X =M.sub.XR /(ΣFxdis)

in which: M_(XR) denotes the last calculated value of the mass of theconstituent X present in the reactor R; Σ Fxdis denotes the sum of allthe mass flow rates Fxdis at which the constituent X disappears from thereactor R, including by reaction and/or by leaving the reactor; thefunction y=LAG (u, τ) is the solution of the differential equation##EQU12## calculated with the instantaneous value of u and of τ, andwith the last calculated value of y.
 2. Control method according toclaim 1, in which the set point of at least one controlled variable(C_(GR)) is corrected on the basis of the deviation between themeasurement (M_(GR)) and the prediction (P_(GR)) of this controlledvariable, so as to make the control effictive even in the presence of anerror in the prediction of this controlled variable (P_(GR)).
 3. Controlmethod according to claim 1, in which the model (M) of the process isperiodically adapted on the basis of the deviation between thepredictions (P_(GR)) and the measurements (M_(GR)) of the controlledvariables, such that the model of the process should supply predictionsof the controlled variables (P_(GR)) which are as near as possible tothe measurements of these variables (M_(GR)).
 4. Control methodaccording to claim 3, in which the measurements (M_(GR)) of thecontrolled variables are involved only in the optional adaptation of themodel of the process and are not directly involved in the calculation ofthe set points of the manipulated variables of the process (C_(GC)). 5.Control method according to claim 1, applied to a polymerizationprocess, including one or more of the following additionalsteps:calculation of a set point of temperature in the reactor as afunction of one or more set points of the product properties; andtransmission of this temperature set point to one or more actuatorsmaking it possible to modify the temperature in the reactor; calculationof a heat balance for the reactor, based especially on temperaturemeasurements; use of this heat balance so as to determine the quantityof polymer synthesized per time unit and/or the catalyst efficiencyand/or the concentration of at least one reactant in the reactor;calculation of the quantity of heat produced by the polymerization, by acalculation of the quantity of the reactant or reactants whichpolymerize; determination by this means of the quantity of heat whichmust be added or removed to maintain the reactor temperature; use of theresult of the said calculation to improve the temperature control, so asto conform as well as possible to the set point of temperature,especially in the case of changes in the production rate.
 6. Controlmethod according to claim 1, in which the property Px_(R) of aconstituent "x" in the reactor R, assimilated to a perfectly mixedreactor, is calculated as follows:

    Px.sub.R =LAG(Px.sub.IN, Mx.sub.R /Fx.sub.IN)

where "Px" is a property of a constituent "x", correspondingsubstantially to the linear mixing law Px₁₊₂ =w₁ ·Px₁ +w₂ ·Px₂, w₁ andw₂ being the mass fractions of two mixed fractions 1 and 2 of propertyPx₁ and Px₂ ; Px₁₊₂ is the property of x as it leaves the reactor aftermixing; Px_(IN) is the property of the constituent "x" as it enters thereactor R; Mx_(R) is the mass of the constituent x in the reactor R;Fx_(IN) is the mass flow rate of the constituent x entering the reactorR.
 7. Control method according to claim 1, including the followingsteps:input of set points relating to one or more properties of theproduct to be synthesized, into a master algorithm; input of the setpoint of the production rate of the process into a slave algorithm;computation of the set points of concentration of the constituents inthe reactor with the master algorithm, especially as a function of theset points and of the measurements of the product properties and ofmeasurements or predictions of the concentrations of the variousconstituents in the reactor; transmission of the set points ofconcentration which are calculated by the master algorithm as inputvariables into the slave algorithm; computation of flow rate set pointsof the constituents entering the reactor, with the slave algorithm,especially as a function of the set point of the process productionrate, of concentration set points and of flow rate measurements of theconstituents entering the reactor, and transmission of the flow rate setpoints which are calculated with the slave algorithm to one or moreactuators in order to control the flow rates of the constituentsentering the reactor,in which the master algorithm and/or the slavealgorithm are used in accordance with one of the preceding claims. 8.Control method according to claim 7, characterized in that the masteralgorithm includes:a prediction unit based on a direct model of theprocess allowing to supply a prediction of the properties of thesynthesized product as a function of measurements and/or of predictionsof the concentrations of the constituents; an adaptation unit comparingthe predictions of properties calculated by the prediction unit withvalues actually measured on the synthesized product and derivingadaptation parameters from this comparison, the said adaptationparameters being involved as additional inputs into the said predictionunit of the master algorithm; and a control unit based on a reversemodel of the process, for computing, as a function of the set points andof the predictions of properties of the product to be synthesized,concentrations set points for the slave algorithm, the said adaptationparameters also being involved as additional inputs into the saidcontrol unit.
 9. Control method according to claim 8 applied to apolymerization process, in which:the melt index (MI) and/or the standarddensity (SD) of the polymer and/or its comonomer content are measuredperiodically; the prediction unit of the master algorithm calculates rawpredictions of MI and of SD as a function of the temperature in thereactor, of the concentrations in the reactor and of the residence timein the various units of equipment in the polymerization circuit;periodically, the adaptation unit of the master algorithm:resynchronizesthe raw predictions of MI and SD, taking into account the time elapsedbetween the taking of the measurements of MI and SD and obtaining theresult of the measurements, and compares the resynchronized rawpredictions of MI and SD with the measurements of MI and SD, calculatesa multiplicative adaptation parameter kMI applied to the raw predictionof the MI to obtain a calibrated prediction of the MI, and calculates anadditive adaptation parameter kSD applied to the raw prediction of SD toobtain a calibrated prediction of SD.
 10. Control method according toclaim 7, in which the slave algorithm includes:a prediction unit basedon a direct model of the process allowing to supply a prediction of theconcentrations of one or more of the constituents, based on a materialbalance in the reactor; an adaptation unit comparing the predictions ofconcentrations calculated by the direct model with measurements ofconcentration and deriving adaptation parameters from this comparison,the said adaptation parameters being involved as additional inputs intothe said prediction unit of the slave algorithm; and a control unitbased on a reverse model of the process, for computing, as a function ofthe production rate set point, of the concentration set points computedby the control unit of the master algorithm and of the predictions ofconcentration which are computed by the prediction unit of the slavealgorithm, the set points for the flows entering the reactor, the saidadaptation parameters being involved as additional inputs into the saidcontrol unit of the slave algorithm.
 11. Control method according toclaim 10, in which the adaptation unit of the slave algorithm comparesthe measurements of the concentrations of propylene (Pe), hydrogen (Hy)and/or optional comonomer (Et) with the values predicted by theprediction unit of the slave algorithm, so as to determine at least oneof the following adaptation parameters:a) the specific activity of thecatalyst for propylene "APe", in kg/h of polypropylene per kg ofcatalyst and per kg/m³ of propylene; b) the gain error in themeasurement of hydrogen flow rate "KfHy"; c) the purity of the comonomerfeed "KfEt".
 12. Control method according to claim 1, applied to thecontrol of the continuous synthesis of polyethylene by polymerization ofethylene in at least one reactor, the reactants including ethylene,hydrogen and/or an optional comonomer, the polymerization reactiontaking place in the presence of a catalyst and part of the content ofthe reactor being continuously or intermittently removed.
 13. Controlmethod according to claim 10, in which the adaptation unit of the slavealgorithm compares the measurements of the concentrations of ethylene(Et), hydrogen (Hy) and/or optional comonomer (Bt) with the valuespredicted by the prediction unit of the slave algorithm, so as todetermine at least one of the following adaptation parameters:a) thespecific activity of the catalyst for ethylene "AEt", in kg/h ofpolyethylene per kg of catalyst and per kg/m³ of ethylene; b) the gainerror in the measurement of flow rate of hydrogen "KfHy"; c) the purityof the comonomer feed "KfBt".
 14. The control method according to claim12, wherein the adaptation unit of the slave algorithm compares themeasurements of the concentrations of ethylene (Et), hydrogen (Hy)and/or optional comonomer (Bt) with the values predicted by theprediction unit of the slave algorithm, so as to determine at least oneof the following adaptation parameters:a) the specific activity of thecatalyst for ethylene "AEt", in kg/h of polyethylene per kg of catalystand per kg/m³ of ethylene; b) the gain error in the measurement of theflow rate of hydrogen "KfHy"; or c) the purity of the comonomer feed"KfBt".
 15. Control method according to claim 1, applied to the controlof the continuous synthesis of polypropylene by polymerization ofpropylene in at least one reactor, the reactants including propylene,hydrogen and/or an optional comonomer, the polymerization reactiontaking place in the presence of a catalyst and part of the content ofthe reactor being continuously or intermittently removed.
 16. Thecontrol method according to claim 15, wherein the adaptation unit of theslave algorithm compares the measurements of the concentrations ofpropylene (Pe), hydrogen (Hy) and/or optional comonomer (Et) with thevalues predicted by the prediction unit of the slave algorithm, so as todetermine at least one of the following adaptation parameters:a) thespecific activity of the catalyst for propylene "APe", in kg/h ofpolypropylene per kg of catalyst and per kg/m³ of propylene; b) the gainerror in the measurement of hydrogen flow rate "KfHy"; or c) the purityof the comonomer feed "KfEt".
 17. Control method according to claim 1,applied to a polymerization process, in which one or more properties ofthe polymer are evaluated by employing a technique chosen from nearinfrared spectroscopy (NIR), Fourier transform infrared spectroscopy(FTIR) and a nuclear magnetic resonance (NMR).
 18. Control methodaccording to claim 1, applied to a polymerization process, in which oneor more properties of the polymer are evaluated by applying apreestablished correlation relationship to the results of measurementscarried out by near infrared spectroscopy (NIR) at a number ofwavelengths predetermined as a function of the nature of the polymer andchosen between 0.8 and 2.6 um.
 19. A process of synthesis of a chemicalproduct in an apparatus comprising, synthesizing at least one product insaid equipment, wherein said equipment is controlled by means of thecontrol method according to claim
 1. 20. The control method of claim 1,wherein the set points of the process manipulated variables aretransmitted to control units controlling the actuators.
 21. A devise forcontrolling a chemical synthesis process in a synthesis apparatus,comprising:at least one mixed reactor; at least one means for inputtinga set point of property (CGR) of the product to be synthesized into thecomputing unit; at least one means for inputting a set point of aproduction rate of the product to be synthesized (CGC) into thecomputing unit; at least one control unit (OC); at least one predictionunit (OP); at least one means for imposing a control variable (CGC) on asuitable actuator,wherein the prediction unit (OP) is designed in such away that the mass M_(XR) of at least one constituent (X) in the reactor(R) is predicted by the equation:

    M.sub.XR =LAG(F.sub.XRin ·τ.sub.X, τ.sub.x)

in which: F_(XRin) is the mass flow rate of the constituent X enteringthe reactor R; τ_(X) is the residence time of X in the reactor, thevalue of which is

    τ.sub.X =M.sub.XR /(ΣFxdis)

in which: M_(XR) denotes the last calculated value of the mass of theconstituent X present in the reactor R; Σ Fxdis denotes the sum of allthe mass flow rates Fxdis at which the constituent X disappears from thereactor R, especially by reaction and/or by leaving the reactor; thefunction y=LAG (u, τ) is the solution of the differential equation##EQU13## calculated with the instantaneous value of u and of τ, andwith the last calculated value of y wherein the prediction unit (OP) isbased on a mathematical model of the process (M); and calculated withthe instantaneous value of u and of τ and with the last calculated valueof y.